Decimal to Fraction Calculator
Turn any decimal into a simplified fraction (and mixed number), with denominators up to 10,000.
How it works
0.625 = 625/1000, then divide top and bottom by their GCF (125) to get 5/8
A terminating decimal is a fraction over a power of ten, so the direct route is to put the digits over 10, 100, 1000… and reduce. This calculator goes one better: it searches (using continued fractions) for the closest fraction with a denominator of at most 10,000, which is how 0.333333 comes back as 1/3 rather than 333333/1000000.
Worked example
0.625 = 625/1000. The greatest common factor of 625 and 1000 is 125, and dividing both by it gives 5/8. Check: 5 ÷ 8 = 0.625 exactly.
Frequently asked questions
Why did 0.333333 come back as 1/3?
The calculator looks for the simplest fraction within a tiny tolerance of your input, not just the digits over a power of ten. 1/3 is far simpler than 333333/1000000 and matches to six decimal places.
What about a decimal like 0.1 that computers store imperfectly?
Binary floating point can’t hold 0.1 exactly, but the search tolerance absorbs that error, so you still get the intended 1/10.
How do I convert a repeating decimal by hand?
Use algebra: for x = 0.727272…, multiply by 100 to get 100x = 72.7272…, subtract to get 99x = 72, so x = 72/99 = 8/11.
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This calculator is for educational purposes. Double-check important results before acting on them.